Question

In a machine shop, two cams are produced, one of aluminum and one of iron. Both cams have the same mass. Which cam is larger? (a) the aluminum cam (b) the iron cam (c) Both cams have the same size.

Answer 1

The aluminium cam. Aluminium is much lighter than iron, so for them to be the same mass, there would have to be a lot more aluminium.

Answer 2

Oh, I thought other way around, aluminum density is low than iron, so \[density = mass \div volume\] mass is equal. volume must be high.

Answer 3

Yeah... soooo... aluminium ;)
\[\Large \rho = \frac{m}{V}\]
The masses are the same, but the density of aluminium is much lower. Therefore, the volume must be greater for the density to be lower.

Answer 4

Just say the cams each weigh 10kg (I think it'd really be much less than this, but for example's sake). According to Google, the density of iron is about 7.86g/cm^3 and aluminium about 2.7g/cm^3. Note the units too.
\[\Large \begin{array}{l}
\rho = \frac{m}{V}\\
{\rho _{Fe}} = \frac{{{{10}^3}}}{{{V_{Fe}}}} = 7.86{\rm{g}} \cdot {\rm{c}}{{\rm{m}}^{ - 3}}\\
{\rho _{Al}} = \frac{{{{10}^3}}}{{{V_{Al}}}} = 2.7{\rm{g}} \cdot {\rm{c}}{{\rm{m}}^{ - 3}}\\
{V_{Fe}} = \frac{{{{10}^3}}}{{{\rho _{Fe}}}} = \frac{{{{10}^3}}}{{7.86}} = 127.23{\rm{c}}{{\rm{m}}^3}\\
{V_{Al}} = \frac{{{{10}^3}}}{{{\rho _{Al}}}} = \frac{{{{10}^3}}}{{2.7}} = 370.37{\rm{c}}{{\rm{m}}^3}
\end{array}\]
So there's a substantially greater volume of aluminium than iron.